Complex Manifolds and the connection between Music, Geometry of Numbers and Random Functions

Dmitri Panov and Igor Wigman, both Professors of Mathematics, presented on the ground-breaking research accomplished through their careers. The Inaugural Lecture Series from the Faculty of Natural, Mathematical & Engineering Sciences (NMES) celebrates the journeys and career successes of our professors, to provide insight and inspiration from the faculty's leading scientists. ---------------------------------- The geometrisation of complex manifolds by Professor Dmitri Panov Every surface possesses its favourite metric: curvature one for a sphere, flat for a torus, and hyperbolic for surfaces of high genus. It is geometers' dream to generalise this fact by finding canonical metrics on other manifolds. The lecture focused on two such instances: polyhedral Kähler manifolds, i.e. complex manifolds glued from simplices, and spherical surfaces, i.e. surfaces glued from spherical triangles. The geometry of numbers, random functions, and music by Professor Igor Wigman professor Igor Wigman shared an overview of his research drawing inspiration from three classical subjects within mathematics and revealing a surprising link that unites all of them: Geometry of numbers, Geometry of typical functions and Geometry of music. He explored the geometry of numbers and how this field of study offers techniques for solving problems related to counting and understanding sets of numbers that are distinct from each other. He looked at a behaviour of “typical” functions, both in one and higher dimensions. Igor also explored how sound moves through space by analysing the spectrum of frequencies music creates, dissecting why instruments like guitars and violins produce distinct tones at the same frequency, to look at the forces underpinning the geometry of music. ---------------------------------- 00:00 - 2:53 Welcome from Mark French 2:54 - 26:33 The geometrisation of complex manifolds by Professor Dmitri Panov 26:34 - 29:14 Vote of Thanks 29:15 - 1:01:24 The geometry of numbers, random functions, and music by Professor Igor Wigman 1:01:25 - 1:07:13 Vote of Thanks 1:07:14 Closing remarks ---------------------------------- Upcoming Inaugural Lectures: https://www.kcl.ac.uk/events/series/i...